Okay, so I'm feeling a little silly as I think this was probably something covered in grades 6-8... However, for the life of me I can't think of the solution or find one online aside from the obvious guess work...
I'm writing some software that requires I create a parallelogram out of an existing triangle....
So essentially, I think I need to copy the original triangle and then somehow mirror it to form a parallelogram. I'm just not certain as to what steps need to be taken to transform the copied triangle into the right rotation and attached to the right side of the original triangle to make it a parallelogram...
Here's an image I drew up illustrating what I mean.... https://puu.sh/rIQZC/43c52e9afb.png
Reflect the triangle about the midpoint of one of its sides. An easy way to do this is to reflect the vertex that’s opposite your chosen side and then connect the dots:
Let’s say we want to build the parallelogram with $\overline{AC}$ as its diagonal. Find its midpoint $M$, draw the line $BM$ and measure off a distance equal to $|\overline{BM}|$ on the other side of $M$. That’s the fourth vertex of your parallelogram:
Analytically, $M=(A+C)/2$ and $B'=M-(B-M)$, i.e., reverse the vector $\vec{MB}$. This construction can be performed on any side of the triangle, of course.
By the way, this is equivalent to rotating a copy of the triangle 180° and then translating it so that the edges that you want to be the diagonal of the parallelogram coincide.